Related papers: On some tensor inequalities based on the t-product
The main objective of present investigation to obtain some Minkowski-type fractional integral inequalities using generalised proportional Hadamard fractional integral operators which is introduced by Rahman et al in the paper (certain…
In the current note, we investigate the mathematical relations among the weighted arithmetic mean-geometric mean (AM-GM) inequality, the H\"{o}lder inequality and the weighted power-mean inequality. Meanwhile, the proofs of mathematical…
In [13], Hillar and Lim famously demonstrated that "multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard". Despite many recent advancements, the state-of-the-art methods for…
We study low T-phase-rank approximation of sectorial third-order tensors $\mathscr{A}\in\mathbb{C}^{n\times n\times p}$ under the tensor T-product. We introduce canonical T-phases and T-phase rank, and formulate the approximation task as…
We investigate Brunn-Minkowski-type inequalities for the torsional rigidity $T_\gamma$ and the first eigenvalue $\lambda_\gamma$ associated with the Ornstein-Uhlenbeck operator. Counterexamples are provided showing that neither concavity…
A generalisation of inner product spaces of an inequality due to Ostrowski and applications for sequences and integrals are given.
In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.
Matrix concentration inequalities, intimately connected to the Non-Commutative Khintchine inequality, have been an important tool in both applied and pure mathematics. We study tensor versions of these inequalities, and establish…
In this note, we present a refinement of the well-known AM-GM inequality. We use this improved inequalty to establish corresponding inequalities on Hilbert space. We also give some refinements of the Kantorovich inequality.
We study the concept of frame in tensor product of n-Hilbert spaces as tensor product of n-Hilbert spaces is again a n-Hilbert space. We generalize some of the known results about bases to frames in this new Hilbert space. A relationship…
In this paper, the Cartan tensors of the $(\alpha,\beta)$-norms are investigated in details. Then an equivalence theorem of $(\alpha,\beta)$-norms is proved. As a consequence in Finsler geometry, general $(\alpha,\beta)$-metrics on smooth…
The algebraic theory of third-order tensors under the $t$-product is naturally formulated over the complex field via Fourier block diagonalization. However, many applications require real-valued representations. In this paper, we…
We obtain new inequalities with alternating signs of H\"{o}lder and Minkowski type.
In recent years several classes of structured matrices are extended to classes of tensors in the context of tensor complementarity problem. The tensor complementarity problem is a class of nonlinear complementarity problem where the…
The mixed-norm versions of the H\"older and Minkowski integral inequalities are used to produce new, general estimates involving symmetric geometric means of mixed norms. Various existing mixed-norm estimates are shown to be simple special…
This article introduces an algebraic framework for establishing eigenvalue bounds for symmetric positive definite tensors by leveraging intrinsic invariants, specifically the trace and determinant (resultant). We derive a hierarchy of…
Various miscellaneous functional inequalities are deduced for the so-called generalized inverse trigonometric and hyperbolic functions. For instance, functional inequalities for sums, difference and quotient of generalized inverse…
A generalisation of the Cassels and Greub-Reinboldt inequalities in complex or real inner product spaces and applications for isotonic linear functionals, integrals and sequences are provided.
Assume that $X$ is a non-empty set and $T$ and $S$ are real or complex mappings defined on the product $X \times X$. Additive and multiplicative Sincov's equations are: $$T(x,z) = T(x, y ) + T(y, z)$$ and $$S(x,z) = S(x, y ) \cdot S(y,…
Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.